The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Performance of the Vitek 2 system software version 5.03 in the bacterial identification and antimicrobial susceptibility test: evaluation study of clinical and reference strains of Gram-positive cocci

Introduction. The genera Enterococcus, Staphylococcus and Streptococcus are recognized as important Gram-positive human pathogens. The aim of this study was to evaluate the performance of Vitek 2 in identifying Gram-positive cocci and their antimicrobial susceptibilities. Methods. One hundred four isolates were analyzed to determine the accuracy of the automated system for identifying the bacteria and their susceptibility to oxacillin and vancomycin. Results. The system correctly identified 77.9% and 97.1% of the isolates at the species and genus levels, respectively. Additionally, 81.8% of the Vitek 2 results agreed with the known antimicrobial susceptibility profiles. Conclusion. Vitek 2 correctly identified the commonly isolated strains; however, the limitations of the method may lead to ambiguous findings.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

The interaction of Gram negative bacteria and S. mansoni in mice with experimental Schistosomiasis

Animals (122 mice) were infected each with eighty cercariae of S. mansoni and subsequently challenged intravenously eight weeks later with the following gram-negative organisms. S. typhi, E. coli, Klebsiella-enterobacter species, Proteus mirabilis and Pseudomonas aeruginosa. Enumeration of bacteria in the liver, spleen and blood and S. mansoni from the portal sistem was performed from one to four weeks later in infected animals. A significant difference between infection produced by S. typhi and other gram negative organisms was observed: S. typhi persisted longer in the spleen and liver and could be recovered from S. mansoni worms up to three weeks following bacterial infection. Other gram negative bacteria disappeared from S. mansoni worms after two weeks of initial challenge. Additional animals (51 mice) infected with S. mansoni were given S. typhi, E. coli or sterile saline. After two weeks, animals were sacrificed and the recovery rate of worms from the portal system, and the mesenteric and hepatic oogram were determined. in animals infected with E. coli a significant decrease in the number of worms was observed compared to the saline control group; thirty worms were recovered in the control group compared to two worms in e. coli infected animals. In addition, the patterns of oviposition was significantly different in these latter animals suggesting complete inhibition of this process. Following S. typhi infection the difference in recovery of worms and pattern of oviposition was minimal. These findings suggest a difference in the interaction of various gram negative bacteria and S. mansoni and are consistent with the clinical observation of prolonged salmonella bacteremia in patients with schistosomiasis.

Macrophage Migration Inhibitory Factor Deficiency Is Associated With Impaired Killing of Gram-Negative Bacteria by Macrophages and Increased Susceptibility to Klebsiella pneumoniae Sepsis.

The cytokine macrophage migration inhibitory factor (MIF) is an important component of the early proinflammatory response of the innate immune system. However, the antimicrobial defense mechanisms mediated by MIF remain fairly mysterious. In the present study, we examined whether MIF controls bacterial uptake and clearance by professional phagocytes, using wild-type and MIF-deficient macrophages. MIF deficiency did not affect bacterial phagocytosis, but it strongly impaired the killing of gram-negative bacteria by macrophages and host defenses against gram-negative bacterial infection, as shown by increased mortality in a Klebsiella pneumonia model. Consistent with MIF's regulatory role of Toll-like 4 expression in macrophages, MIF-deficient cells stimulated with lipopolysaccharide or Escherichia coli exhibited reduced nuclear factor κB activity and tumor necrosis factor (TNF) production. Addition of recombinant MIF or TNF corrected the killing defect of MIF-deficient macrophages. Together, these data show that MIF is a key mediator of host responses against gram-negative bacteria, acting in part via a modulation of bacterial killing by macrophages.

On the zeroes of Goss polynomials

"Vegeu el resum a l'inici del document del fitxer adjunt."

Granular layer in the periplasmic space of gram-positive bacteria and fine structures of Enterococcus gallinarum and Streptococcus gordonii septa revealed by cryo-electron microscopy of vitreous sections.

High-resolution structural information on optimally preserved bacterial cells can be obtained with cryo-electron microscopy of vitreous sections. With the help of this technique, the existence of a periplasmic space between the plasma membrane and the thick peptidoglycan layer of the gram-positive bacteria Bacillus subtilis and Staphylococcus aureus was recently shown. This raises questions about the mode of polymerization of peptidoglycan. In the present study, we report the structure of the cell envelope of three gram-positive bacteria (B. subtilis, Streptococcus gordonii, and Enterococcus gallinarum). In the three cases, a previously undescribed granular layer adjacent to the plasma membrane is found in the periplasmic space. In order to better understand how nascent peptidoglycan is incorporated into the mature peptidoglycan, we investigated cellular regions known to represent the sites of cell wall production. Each of these sites possesses a specific structure. We propose a hypothetic model of peptidoglycan polymerization that accommodates these differences: peptidoglycan precursors could be exported from the cytoplasm to the periplasmic space, where they could diffuse until they would interact with the interface between the granular layer and the thick peptidoglycan layer. They could then polymerize with mature peptidoglycan. We report cytoplasmic structures at the E. gallinarum septum that could be interpreted as cytoskeletal elements driving cell division (FtsZ ring). Although immunoelectron microscopy and fluorescence microscopy studies have demonstrated the septal and cytoplasmic localization of FtsZ, direct visualization of in situ FtsZ filaments has not been obtained in any electron microscopy study of fixed and dehydrated bacteria.

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

Transcriptional profiling of Gram-positive Arthrobacter in the phyllosphere: induction of pollutant degradation genes by natural plant phenolic compounds.

Arthrobacter chlorophenolicus A6 is a Gram-positive, 4-chlorophenol-degrading soil bacterium that was recently shown to be an effective colonizer of plant leaf surfaces. The genetic basis for this phyllosphere competency is unknown. In this paper, we describe the genome-wide expression profile of A.chlorophenolicus on leaves of common bean (Phaseolus vulgaris) compared with growth on agar surfaces. In phyllosphere-grown cells, we found elevated expression of several genes known to contribute to epiphytic fitness, for example those involved in nutrient acquisition, attachment, stress response and horizontal gene transfer. A surprising result was the leaf-induced expression of a subset of the so-called cph genes for the degradation of 4-chlorophenol. This subset encodes the conversion of the phenolic compound hydroquinone to 3-oxoadipate, and was shown to be induced not only by 4-chlorophenol but also hydroquinone, its glycosylated derivative arbutin, and phenol. Small amounts of hydroquinone, but not arbutin or phenol, were detected in leaf surface washes of P.vulgaris by gas chromatography-mass spectrometry. Our findings illustrate the utility of genomics approaches for exploration and improved understanding of a microbial habitat. Also, they highlight the potential for phyllosphere-based priming of bacteria to stimulate pollutant degradation, which holds promise for the application of phylloremediation.

The structure of nervous tissue and of Gram-positive bacteria studied by cryo-electron microscopy of vitreous sections

Résumé La structure, ou l'architecture, des êtres vivants définit le cadre dans lequel la physique de la vie s'accomplit. La connaissance de cette structure dans ses moindres détails est un but essentiel de la biologie. Son étude est toutefois entravée par des limitations techniques. Malgré son potentiel théorique, la microscopie électronique n'atteint pas une résolution atomique lorsqu'elle est appliquée ä la matièxe biologique. Cela est dû en grande partie au fait qu'elle contient beaucoup d'eau qui ne résiste pas au vide du microscope. Elle doit donc être déshydratée avant d'être introduite dans un microscope conventionnel. Des artéfacts d'agrégation en découlent inévitablement. La cryo-microscopie électronique des sections vitreuses (CEMOVIS) a ëté développée afin de résoudre cela. Les spécimens sont vitrifiés, c.-à-d. que leur eau est immobilisée sans cristalliser par le froid. Ils sont ensuite coupés en sections ultrafines et celles-ci sont observées à basse température. Les spécimens sont donc observés sous forme hydratée et non fixée; ils sont proches de leur état natif. Durant longtemps, CEMOVIS était très difficile à exécuter mais ce n'est plus le cas. Durant cette thèse, CEMOVIS a été appliqué à différents spécimens. La synapse du système nerveux central a été étudiée. La présence dans la fente synaptique d'une forte densité de molécules organisées de manière périodique a été démontrée. Des particules luminales ont été trouvées dans Ies microtubules cérébraux. Les microtubules ont servi d'objets-test et ont permis de démontrer que des détails moléculaires de l'ordre du nm sont préservés. La compréhension de la structure de l'enveloppe cellulaire des bactéries Grampositives aété améliorée. Nos observations ont abouti à l'élaboration d'un nouveau modèle hypothétique de la synthèse de la paroi. Nous avons aussi focalisé notre attention sur le nucléoïde bactérien et cela a suscité un modèle de la fonction des différents états structuraux du nucléoïde. En conclusion, cette thèse a démontré que CEMOVIS est une excellente méthode poux étudier la structure d'échantillons biologiques à haute résolution. L'étude de la structure de divers aspects des êtres vivants a évoqué des hypothèses quant à la compréhension de leur fonctionnement. Summary The structure, or the architecture, of living beings defines the framework in which the physics of life takes place. Understanding it in its finest details is an essential goal of biology. Its study is however hampered by technical limitations. Despite its theoretical potential, electron microscopy cannot resolve individual atoms in biological matter. This is in great part due to the fact. that it contains a lot of water that cannot stand the vacuum of the microscope. It must therefore be dehydrated before being introduced in a conventional mìcroscope. Aggregation artefacts unavoidably happen. Cryo-electron microscopy of vitreous sections (CEMOVIS) has been developed to solve this problem. Specimens are vitrified, i.e. they are rapidly cooled and their water is immobilised without crystallising by the cold. They are then. sectioned in ultrathin slices, which are observed at low temperatures. Specimens are therefore observed in hydrated and unfixed form; they are close to their native state. For a long time, CEMOVIS was extremely tedious but this is not the case anymore. During this thesis, CEMOVIS was applied to different specimens. Synapse of central nervous system was studied. A high density of periodically-organised molecules was shown in the synaptic cleft. Luminal particles were found in brain microtubules. Microtubules, used as test specimen, permitted to demonstrate that molecular details of the order of nm .are preserved. The understanding of the structure of cell envelope of Gram-positive bacteria was improved. Our observations led to the elaboration of a new hypothetic model of cell wall synthesis. We also focused our attention on bacterial nucleoids and this also gave rise to a functional model of nucleoid structural states. In conclusion, this thesis demonstrated that CEMOVIS is an excellent method for studying the structure of bìologìcal specimens at high resolution. The study of the structure of various aspects of living beings evoked hypothesis for their functioning.

Recognition of Gram-positive Intestinal Bacteria by Hybridoma- and Colostrum-derived Secretory Immunoglobulin A Is Mediated by Carbohydrates.

Humans live in symbiosis with 10(14) commensal bacteria among which >99% resides in their gastrointestinal tract. The molecular bases pertaining to the interaction between mucosal secretory IgA (SIgA) and bacteria residing in the intestine are not known. Previous studies have demonstrated that commensals are naturally coated by SIgA in the gut lumen. Thus, understanding how natural SIgA interacts with commensal bacteria can provide new clues on its multiple functions at mucosal surfaces. Using fluorescently labeled, nonspecific SIgA or secretory component (SC), we visualized by confocal microscopy the interaction with various commensal bacteria, including Lactobacillus, Bifidobacteria, Escherichia coli, and Bacteroides strains. These experiments revealed that the interaction between SIgA and commensal bacteria involves Fab- and Fc-independent structural motifs, featuring SC as a crucial partner. Removal of glycans present on free SC or bound in SIgA resulted in a drastic drop in the interaction with Gram-positive bacteria, indicating the essential role of carbohydrates in the process. In contrast, poor binding of Gram-positive bacteria by control IgG was observed. The interaction with Gram-negative bacteria was preserved whatever the molecular form of protein partner used, suggesting the involvement of different binding motifs. Purified SIgA and SC from either mouse hybridoma cells or human colostrum exhibited identical patterns of recognition for Gram-positive bacteria, emphasizing conserved plasticity between species. Thus, sugar-mediated binding of commensals by SIgA highlights the currently underappreciated role of glycans in mediating the interaction between a highly diverse microbiota and the mucosal immune system.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced